• CHESS ANALYTICS 00: Methods: Measuring World-Championship Roads with Stockfish 18 WDL
• CHESS ANALYTICS 00.0: List of Other Chess Analytics Articles

1. 1. Short verdict
2. 2. Overall metric table
3. 3. Accuracy, PQ, and dominance
4. 4. Loss metrics: Karpov slightly cleaner
5. 5. Standard deviations and stability
6. 6. Game Accuracy and Mutual Accuracy
7. 7. Game-by-game metric edge
8. 8. Phase-by-phase interpretation
   1. Games 1–9: Karpov builds the match
   2. Games 1–27: Karpov’s lead phase
   3. Games 28–48: Kasparov takes over
   4. Games 47–48: the collapse/reversal endpoint
9. 9. Correlations with game score
10. 10. Which metric families explain the 25–23 result?
    1. 1. Conversion explains most of the final margin
    2. 2. Expected Score and Dominance explain the underlying edge
    3. 3. Volatility explains Karpov’s stable advantage
    4. 4. RMS ES Loss is more favorable than raw accuracy counts
    5. 5. Error Concentration is almost irrelevant here
11. 11. Chess interpretation
12. 12. Final article-style thesis

I treated Anatoly Karpov as the main player and Garry Kasparov as the opponent, because that is how the uploaded run tables are structured. This package covers the single Karpov–Kasparov 1984 World-Championship match, so “match-by-match” and “overall” are numerically the same; I add phase-by-phase readings to make the long 48-game match interpretable.

1. Short verdict

The 1984 match is statistically almost equal, but with a small Karpov edge in the aggregate.

The most important result is this:

Karpov won the 48-game point score 25–23, but the engine-WDL expected score was only 24.187–23.813.

So Karpov’s actual margin was +2.000, but his expected-score margin was only +0.374. The rest came from conversion:

Actual score margin = Expected-score margin + Conversion swing
+2.000 = +0.374 + +1.626

That means the match was not decided by a large average engine-quality gap. It was decided by:

1. Tiny Karpov average superiority
2. Slightly lower Karpov volatility
3. Slightly better Karpov loss profile
4. Much better Karpov conversion over the full match
5. A major phase reversal where Kasparov became better late

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2. Overall metric table

Metric	Karpov	Kasparov	Difference / ratio	Better
Score	25.000	23.000	+2.000 / 1.087×	Karpov
Expected Score	24.187	23.813	+0.374 / 1.016×	Karpov
Conversion	+0.813	−0.813	+1.626 difference	Karpov
WDL Accuracy	98.633	98.563	+0.070 / 1.0007×	Karpov
Performance Quality / PQ	97.601	97.580	+0.021 / 1.0002×	Karpov
Dominance	+0.023	−0.023	+0.046 difference	Karpov
Mean ES Loss	0.01367	0.01437	Karpov 4.9% lower	Karpov
RMS ES Loss	0.03546	0.03611	Karpov 1.8% lower	Karpov
Error Concentration	2.583	2.589	Karpov 0.2% lower	Almost equal
WDL Volatility	0.01441	0.01528	Karpov 5.7% lower	Karpov
Total WDL Volatility	23.985	25.555	Karpov 6.1% lower	Karpov
HardRAP	2439.65	2248.66	Karpov 1.085×	Karpov
SoftRAP	3562.24	3466.24	Karpov 1.028×	Karpov

The striking feature is how small most differences are. Karpov wins almost every aggregate category, but usually by microscopic margins.

The only large-looking edge is conversion: Karpov scored +0.813 above expected, while Kasparov scored −0.813 below expected. That conversion swing of +1.626 explains most of the final 25–23 point margin.

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3. Accuracy, PQ, and dominance

Metric	Karpov	Kasparov	Difference
WDL Accuracy	98.633	98.563	+0.070
PQ	97.601	97.580	+0.021
Dominance	+0.023	−0.023	+0.046

These are not domination numbers. They say:

Karpov was slightly better on average, but the match was nearly level in raw move-quality terms.

The dominance figure is especially small. A dominance difference of +0.046 over 48 games is much lower than Karpov’s clearer wins against Korchnoi in 1981, or Fischer’s run-wide dominance in 1971–72. This match was a long technical deadlock with a small early Karpov surplus.

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4. Loss metrics: Karpov slightly cleaner

Metric	Karpov	Kasparov	Ratio
Mean ES Loss	0.01367	0.01437	0.951
RMS ES Loss	0.03546	0.03611	0.982
Error Concentration	2.583	2.589	0.998
WDL Volatility	0.01441	0.01528	0.943

Karpov’s most meaningful non-score edges are:

• Mean ES Loss: about 4.9% lower
• WDL Volatility: about 5.7% lower
• Total Volatility: about 6.1% lower

But RMS ES Loss and Error Concentration are almost equal. This means Karpov did not massively outperform Kasparov in large-error avoidance. Instead, he was marginally more stable and marginally less leaky.

In plain chess language:

Karpov’s aggregate edge was not “Kasparov blundered much more.”
It was “Karpov leaked slightly less expected score and kept the match slightly less volatile.”

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5. Standard deviations and stability

Metric SD	Karpov	Kasparov	SD ratio
WDL Accuracy SD	5.813	6.257	0.929
PQ SD	2.434	2.566	0.949
Mean ES Loss SD	0.0581	0.0626	0.929
RMS ES Loss SD	0.0387	0.0415	0.933
Error Concentration SD	1.036	1.010	1.025
WDL Volatility SD	0.0581	0.0629	0.924
Total Volatility SD	0.595	0.675	0.882
HardRAP SD	19.477	19.671	0.990
SoftRAP SD	9.873	10.210	0.967

Karpov was usually slightly more stable. His WDL Accuracy, PQ, Mean ES Loss, RMS ES Loss, Volatility, and Total Volatility SDs are all lower.

The one exception is Error Concentration SD, where Karpov is slightly higher: 1.036 vs 1.010. So Kasparov’s error concentration was marginally more stable, even though Karpov’s average error concentration was infinitesimally better.

The stability conclusion:

Karpov was the steadier player in most categories, but only slightly.
This was not a mismatch of consistency; it was a match of two extremely stable players.

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6. Game Accuracy and Mutual Accuracy

The game-level aggregate values are:

Game-level metric	Mean	SD	Min	Max
Game Accuracy	98.780	1.285	93.947	99.888
Mutual Accuracy	97.589	2.513	88.259	99.776
Game Mean ES Loss	0.01220	0.01285	0.00112	0.06058
Game RMS ES Loss	0.03672	0.03960	0.00313	0.13545
Game Volatility	0.01305	0.01317	0.00150	0.06204
Game Total Volatility	1.032	1.267	0.0735	5.3975
Game Conversion Magnitude	0.119	0.211	0.0006	0.7435

This is an extremely high-quality match by average Game Accuracy and Mutual Accuracy. But high game quality did not mean equal score production in every phase. The match had many near-perfect draws, then decisive moments where conversion and late-match fatigue/pressure mattered.

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7. Game-by-game metric edge

Across the 48 games:

Metric family	Karpov better	Kasparov better
WDL Accuracy	23	25
PQ	23	25
Dominance	23	25
Mean ES Loss	23	25
RMS ES Loss	27	21
Volatility	28	20

This is very revealing.

Kasparov actually has the better game-by-game count in raw accuracy, PQ, dominance, and mean loss: 25–23. But Karpov wins the overall match score and has the aggregate expected-score edge.

Why? Because Karpov’s good games were more score-effective earlier, while Kasparov’s late superiority reduced the margin but did not fully overturn it.

Karpov’s clearest game-count advantages are:

• RMS ES Loss: 27–21
• Volatility: 28–20

So if one wants a compact “Karpov edge” from the game-level table, it is not raw accuracy. It is:

fewer severe-loss profiles and lower volatility in more games.

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8. Phase-by-phase interpretation

Because this is one long match, the phase split is more informative than the single-match aggregate.

Games 1–9: Karpov builds the match

Metric	Karpov	Kasparov
Score	6.5	2.5
Expected Score	5.372	3.628
Conversion	+1.128	−1.128
WDL Accuracy	98.154	97.681
PQ	96.126	95.665
Mean ES Loss	0.01846	0.02319
RMS ES Loss	0.05624	0.07209
Volatility	0.01913	0.02391
Dominance	+0.473	−0.473

This was Karpov’s strongest phase. He had:

• large score margin
• large expected-score margin
• strong conversion
• lower mean loss
• lower RMS loss
• lower volatility
• clear dominance

The early match explains much of the final result. Karpov’s final +2 margin survives because he built a large early lead.

Games 1–27: Karpov’s lead phase

Metric	Karpov	Kasparov
Score	16.0	11.0
Expected Score	14.415	12.585
Conversion	+1.585
WDL Accuracy	98.937	98.827
PQ	97.843	97.737
Mean ES Loss	0.01063	0.01173
RMS ES Loss	0.03260	0.03488
Volatility	0.01126	0.01237
Dominance	+0.110

Through game 27, Karpov was clearly ahead both in score and expected score. The actual lead was +5, while expected score gave him about +1.83. Again, conversion was doing a lot of work.

Games 28–48: Kasparov takes over

Metric	Karpov	Kasparov
Score	9.0	12.0
Expected Score	9.772	11.228
Conversion	−0.772
WDL Accuracy	98.603	98.692
PQ	97.289	97.378
Mean ES Loss	0.01397	0.01308
RMS ES Loss	0.03914	0.03770
Volatility	0.01491	0.01444
Dominance	−0.089

This is the reversal. From game 28 onward, Kasparov was better in:

• score
• expected score
• accuracy
• PQ
• mean loss
• RMS loss
• volatility
• dominance

So the overall match cannot be described simply as “Karpov outplayed Kasparov.” More accurately:

Karpov outplayed Kasparov early and converted heavily; Kasparov outplayed Karpov late but did not quite erase the earlier deficit.

Games 47–48: the collapse/reversal endpoint

Metric	Karpov	Kasparov
Score	0.0	2.0
Expected Score	0.441	1.559
Conversion	−0.441
WDL Accuracy	97.830	99.065
PQ	96.310	97.527
Mean ES Loss	0.02171	0.00935
RMS ES Loss	0.07635	0.03703
Volatility	0.02365	0.01087
Dominance	−1.236

The final two games are dramatically Kasparov-favored. Karpov’s RMS ES Loss was more than double Kasparov’s, and his volatility was also more than double. These final games are a strong statistical signal of late-match deterioration from Karpov or late-match surge from Kasparov.

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9. Correlations with game score

The strongest game-level correlations with Karpov’s score were:

Predictor	Correlation with Karpov game score
Karpov Conversion	0.897
Karpov Expected Score	0.877
Dominance difference	0.743
Accuracy difference	0.743
Mean ES Loss advantage	0.743
PQ difference	0.742
Volatility advantage	0.671
RMS ES Loss advantage	0.569
Game Accuracy	−0.096
Mutual Accuracy	−0.097

This says the match result was explained most directly by expected score and conversion, then by the relative edge metrics.

As in your previous reports, Game Accuracy and Mutual Accuracy by themselves do not explain the score. A very accurate game can be a draw. What matters for scoring is not absolute cleanliness but relative advantage.

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10. Which metric families explain the 25–23 result?

1. Conversion explains most of the final margin

Karpov’s final margin was +2.000, but his expected-score margin was only +0.374.

So the conversion swing was:

+1.626

That means about 81% of the final score margin comes from conversion beyond expected score.

This makes conversion the most important score-explanation family.

2. Expected Score and Dominance explain the underlying edge

Karpov’s expected-score margin was only:

24.187–23.813

Dominance was also tiny:

+0.023 vs −0.023

So the underlying engine-WDL edge existed, but barely. It was not enough to describe the match as a clear technical victory.

3. Volatility explains Karpov’s stable advantage

Karpov’s WDL Volatility was:

0.01441 vs 0.01528

That is a modest but meaningful advantage: Karpov was about 5.7% less volatile. Total volatility also favored him by 1.570 points.

This is one of the more “Karpovian” results in the table: even in a near-equal match, he was slightly better at suppressing swings.

4. RMS ES Loss is more favorable than raw accuracy counts

Karpov lost the game-count comparison in raw accuracy 23–25, but won RMS ES Loss 27–21. This suggests that even when Kasparov was often a little cleaner game-by-game, Karpov more often avoided the worse large-error profile.

5. Error Concentration is almost irrelevant here

Error Concentration:

Karpov 2.583 vs Kasparov 2.589

This is essentially equal. It is not a major explanation of the match.

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11. Chess interpretation

The match’s statistical personality is very distinctive:

1984 is not a simple Karpov superiority match. It is a two-phase match: Karpov’s early technical and conversion lead versus Kasparov’s late recovery and eventual statistical takeover.

Karpov’s full-match advantages are real but tiny:

• +0.070 WDL Accuracy
• +0.021 PQ
• +0.046 dominance difference
• 4.9% lower Mean ES Loss
• 5.7% lower volatility
• +0.813 conversion

Kasparov’s countercase is also strong:

• He was better in more individual games by raw accuracy/PQ/dominance.
• From game 28 onward, he was better in nearly every key family.
• The final two games were strongly Kasparov-favored.
• The match’s aggregate expected-score gap was only +0.374 for Karpov.

So the best final reading is:

Karpov won the numerical 48-game score because his early superiority and conversion were large enough to survive Kasparov’s late surge.
But the underlying engine-WDL quality gap was tiny, and the late-match trend points strongly toward Kasparov’s adaptation.

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12. Final article-style thesis

A compact thesis for this article part could be:

Karpov–Kasparov 1984 was a match of early Karpov conversion versus late Kasparov adaptation.
Over the full 48 games, Karpov held a tiny aggregate edge in WDL Accuracy, PQ, expected score, volatility, and RAP. But the edge was narrow: the expected-score margin was only 24.187–23.813, while most of the final 25–23 score came from conversion.
The phase split is decisive: Karpov dominated the early match, but Kasparov was the stronger player from roughly game 28 onward, and especially in the final two games. Thus, the match’s statistics support both truths at once: Karpov was still ahead overall, but Kasparov was already overtaking him by the end.